What frequencies are you using on Band-A and Band-B? They will need to be on different bands to work.
Not sure why you would want to do that. Just let the TNC see and ignore all those packets. If you really need this functionality, the D710 supports RIG control to control the two different VFOs. I know that Hamlib support the the D710 today.
Packet12/96 is a classic Command TNC or KISS TNC. If you want to support APRS traffic when in these two modes, you must have some other program to support the APRS stack communications. This list can offer ideas here to you depending on the OS you're running (Direwolf, UIVIew32, APRSICE, Xastir, APRSSA, etc) If you put the D710 into APRS12/APRS96, the radio's TNC handles all the APRS stack communications. At that point, the TNC will only send APRS objects to the serial port but the TNC will no longer support regular TNC Command mode commands.
Are you talking about Open Squelch support? If so, it's not a supported feature (at least on the D710A) as it didn't work quite right. As such, you'll need to set the RX VFO's squelch to the right level for the frequency's noise floor. This is one of the big limitations of the D710's TNC vs. most modern TNCs like KPC3, PK96, Direwolf, etc.